[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/11082#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/11082","headline":"Hilbertraum Tense Product -Wikipedia","name":"Hilbertraum Tense Product -Wikipedia","description":"before-content-x4 \u6a5f\u80fd\u5206\u6790\u306e\u6570\u5b66\u7684\u30b5\u30d6\u30a8\u30ea\u30a2\u306e\u5f62\u6210 Hilbertraum-Sensor\u88fd\u54c1 Hilber Dreams\u304b\u3089\u65b0\u3057\u3044\u30d8\u30eb\u30d7\u306e\u5922\u3092\u307e\u3068\u3081\u308b\u65b9\u6cd5\u3067\u3059\u3002\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306e\u7d14\u7c8b\u306a\u4ee3\u6570\u5f62\u6210\u3067\u306f\u3001\u4e00\u822c\u7684\u306b\u5b8c\u5168\u306a\u90e8\u5c4b\u3092\u624b\u306b\u5165\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u5341\u5206\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u30d0\u30ca\u30c3\u30cf\u9818\u57df\u7406\u8ad6\u3067\u8abf\u67fb\u3055\u308c\u305f\u6ce8\u5c04\u304a\u3088\u3073\u5c04\u5f71\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u3067\u3055\u3048\u3001\u3053\u308c\u306f\u4e00\u822c\u7684\u306b\u5f79\u7acb\u3064\u305f\u3081\u3001\u6a19\u6e96\u306f\u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u306a\u3044\u305f\u3081\u3001\u671b\u307e\u3057\u3044\u7d50\u679c\u306b\u3064\u306a\u304c\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002 after-content-x4 \u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u304c\u3042\u308a\u307e\u3059 c {displaystyle mathbb {c}} -hilber\u306e\u90e8\u5c4b\u306f\u53cc\u7dda\u5f62\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001sesquilinear\u306e\u307f\u3067\u3059\u304c\u3001\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306f\u53cc\u7dda\u5f62\u753b\u50cf\u7528\u306b\u4f5c\u3089\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u30d2\u30eb\u30d0\u30fc\u30c9\u30ea\u30fc\u30e0\u30ba\u306e\u4ee3\u6570\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u3067\u3053\u308c\u3092\u7d99\u7d9a\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002 \u305d\u308c\u304b\u3089\u3001\u3042\u306a\u305f\u306f\u30d2\u30eb\u30d0\u30fc\u306e\u5922\u3092\u5f97\u308b\u305f\u3081\u306b\u5b8c\u4e86\u3059\u308b\u3060\u3051\u3067\u3042\u308b\u3068\u3044\u3046\u4e88\u9632\u7684\u306a\u5922\u3092\u6301\u3063\u3066\u3044\u308b\u3067\u3057\u3087\u3046\u3002\u307e\u3055\u306b\u3053\u306e\u624b\u9806\u304c\u6210\u529f\u3059\u308b\u3053\u3068\u304c\u5224\u660e\u3057\u307e\u3057\u305f\u3002\u4ee5\u4e0b\u3067\u306f\u3001\u591a\u304f\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306b\u3068\u3063\u3066\u3088\u308a\u91cd\u8981\u306a\u8907\u96d1\u306a\u30d2\u30eb\u30d0\u30fc\u306e\u5922\u306e\u307f\u304c\u8003\u616e\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u5b9f\u969b\u306e\u90e8\u5c4b\u306e\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306e\u69cb\u7bc9\u306f\u975e\u5e38\u306b\u4f3c\u3066\u304a\u308a\u3001\u3044\u304f\u3064\u304b\u306e\u8a73\u7d30\u304c\u3055\u3089\u306b\u7c21\u5358\u3067\u3059\u3002 \u306a\u308c after-content-x4 h {displaystyle h} \u3068 k","datePublished":"2020-07-20","dateModified":"2020-07-20","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f9add4085095b9b6d28d045fd9c92c2c09f549a7","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f9add4085095b9b6d28d045fd9c92c2c09f549a7","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/11082","wordCount":9462,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u6a5f\u80fd\u5206\u6790\u306e\u6570\u5b66\u7684\u30b5\u30d6\u30a8\u30ea\u30a2\u306e\u5f62\u6210 Hilbertraum-Sensor\u88fd\u54c1 Hilber Dreams\u304b\u3089\u65b0\u3057\u3044\u30d8\u30eb\u30d7\u306e\u5922\u3092\u307e\u3068\u3081\u308b\u65b9\u6cd5\u3067\u3059\u3002\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306e\u7d14\u7c8b\u306a\u4ee3\u6570\u5f62\u6210\u3067\u306f\u3001\u4e00\u822c\u7684\u306b\u5b8c\u5168\u306a\u90e8\u5c4b\u3092\u624b\u306b\u5165\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u5341\u5206\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u30d0\u30ca\u30c3\u30cf\u9818\u57df\u7406\u8ad6\u3067\u8abf\u67fb\u3055\u308c\u305f\u6ce8\u5c04\u304a\u3088\u3073\u5c04\u5f71\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u3067\u3055\u3048\u3001\u3053\u308c\u306f\u4e00\u822c\u7684\u306b\u5f79\u7acb\u3064\u305f\u3081\u3001\u6a19\u6e96\u306f\u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u306a\u3044\u305f\u3081\u3001\u671b\u307e\u3057\u3044\u7d50\u679c\u306b\u3064\u306a\u304c\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u304c\u3042\u308a\u307e\u3059 c {displaystyle mathbb {c}} -hilber\u306e\u90e8\u5c4b\u306f\u53cc\u7dda\u5f62\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001sesquilinear\u306e\u307f\u3067\u3059\u304c\u3001\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306f\u53cc\u7dda\u5f62\u753b\u50cf\u7528\u306b\u4f5c\u3089\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u30d2\u30eb\u30d0\u30fc\u30c9\u30ea\u30fc\u30e0\u30ba\u306e\u4ee3\u6570\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u3067\u3053\u308c\u3092\u7d99\u7d9a\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002\u305d\u308c\u304b\u3089\u3001\u3042\u306a\u305f\u306f\u30d2\u30eb\u30d0\u30fc\u306e\u5922\u3092\u5f97\u308b\u305f\u3081\u306b\u5b8c\u4e86\u3059\u308b\u3060\u3051\u3067\u3042\u308b\u3068\u3044\u3046\u4e88\u9632\u7684\u306a\u5922\u3092\u6301\u3063\u3066\u3044\u308b\u3067\u3057\u3087\u3046\u3002\u307e\u3055\u306b\u3053\u306e\u624b\u9806\u304c\u6210\u529f\u3059\u308b\u3053\u3068\u304c\u5224\u660e\u3057\u307e\u3057\u305f\u3002\u4ee5\u4e0b\u3067\u306f\u3001\u591a\u304f\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306b\u3068\u3063\u3066\u3088\u308a\u91cd\u8981\u306a\u8907\u96d1\u306a\u30d2\u30eb\u30d0\u30fc\u306e\u5922\u306e\u307f\u304c\u8003\u616e\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u5b9f\u969b\u306e\u90e8\u5c4b\u306e\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306e\u69cb\u7bc9\u306f\u975e\u5e38\u306b\u4f3c\u3066\u304a\u308a\u3001\u3044\u304f\u3064\u304b\u306e\u8a73\u7d30\u304c\u3055\u3089\u306b\u7c21\u5358\u3067\u3059\u3002 \u306a\u308c        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4h {displaystyle h} \u3068 k {displaystyle k} \u4e8c c {displaystyle mathbb {c}}  – \u30d2\u30eb\u30d0\u30fc\u306e\u5922\u3002\u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u306f\u5e38\u306b\u3042\u308a\u307e\u3059 \u27e8 de \u3001 de \u27e9 {displaystyle langle cdot\u3001cdot rangle} \u30d2\u30eb\u30d9\u30eb\u30c8\u30c9\u30ea\u30fc\u30e0\u306e\u540d\u524d\u306f\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3068\u3057\u3066\u8ffd\u52a0\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3068\u8aac\u660e\u3057\u307e\u3057\u305f\u3002\u6b21\u306b\u3001\u6b21\u306e\u3088\u3046\u306b\u8868\u793a\u3067\u304d\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u4ee3\u6570\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1 h \u2299 k {displaystyle hodot k} \u30d7\u30ed\u30d1\u30c6\u30a3\u306b\u306f\u3001\u3061\u3087\u3046\u30691\u3064\u306e\u5c0f\u7bc0\u5f62\u72b6\u304c\u3042\u308a\u307e\u3059 \u27e8 x1\u2297 y1\u3001 x2\u2297 y2\u27e9H\u2297K= \u27e8 x1\u3001 x2\u27e9Hde \u27e8 y1\u3001 y2\u27e9K{displaystyle langle x_ {1} otimes y_ {1}\u3001x_ {2} otimes y_ {2} rangle _ {hotimes k} = langle x_ {1}\u3001x_ {2} rangle _ {h} cdot langle y_ {1}\u3001y_ {2}} \u3059\u3079\u3066\u306e\u305f\u3081\u306b x1\u3001 x2\u2208 h {displaystyle x_ {1}\u3001x_ {2} in h} \u3068 y1\u3001 y2\u2208 k {displaystyle y_ {1}\u3001y_ {2} in k} \u3002 \u5927\u7d71\u9818\u306e\u5922\u306e\u5b8c\u6210 \uff08 h \u2299 k \u3001 \u27e8 de \u3001 de \u27e9 H\u2297K\uff09\uff09 {displayStyle\uff08Hodot K\u3001Langle CDOT\u3001CDOT RANGLE _ {HOTIMES K}\uff09} Hilbertraum-Sensor\u88fd\u54c1\u3092\u610f\u5473\u3057\u307e\u3059 h {displaystyle h} \u3068 k {displaystyle k} \u3068\u4e00\u7dd2\u3067\u3059 h \u2297 k {displaystyle hotimesk} \u5c02\u7528\u3002\u4e00\u90e8\u306e\u8457\u8005\u306f\u4f7f\u7528\u3057\u3066\u3044\u307e\u3059 h \u2297 k {displaystyle hotimesk} \u4ee3\u6570\u7684\u306a\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306e\u305f\u3081\u306b\u3001\u6b21\u306b\u66f8\u304d\u8fbc\u307f\u307e\u3059 h \u2297\u00afk {displaystyle h\u3001{overline {otimes}}\u3001k} \u5b8c\u4e86\u3059\u308b\u305f\u3081\u306b\u3001\u4ed6\u306e\u4eba\u306f\u4f7f\u7528\u3057\u307e\u3059 h \u2297 k {displaystyle hotimesk} \u3053\u306e\u8a18\u4e8b\u3067\u767a\u751f\u3057\u305f\u3088\u3046\u306b\u3001\u4e21\u65b9\u3068\u8ce2\u660e\u306a\u53ef\u80fd\u6027\u306e\u3042\u308b\u3042\u3044\u307e\u3044\u3055\u306e\u305f\u3081\u306b\u3001\u307e\u305f\u306f\u4ee3\u6570\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306e\u5225\u306e\u8868\u8a18\u6cd5\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002 Hilbertraum-Human\u88fd\u54c1\u306f\u3001Hilbertraum-Sorprift\u306e\u591a\u304f\u306e\u30d2\u30eb\u30d0\u30fc\u306e\u5922\u306e\u8a98\u5c0e\u306b\u3088\u3063\u3066\u6700\u7d42\u7684\u306b\u7c21\u5358\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059 H1\u3001 … \u3001 Hn{displaystyle h_ {1}\u3001ldots\u3001h_ {n}} \u62e1\u5f35\u3057\u307e\u3059 H1\u2297 … \u2297 Hn{displaystyle h_ {1} otimes ldots otimes h_ {n}} \u3044\u3064 \uff08 H1\u2297 … \u2297 Hn\u22121\uff09\uff09 \u2297 Hn{displaystyle\uff08h_ {1} otimes ldots otimes h_ {n-1}\uff09otimes h_ {n}}} \u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u6574\u6d41\u3001\u9023\u60f3\u3001\u304a\u3088\u3073\u5206\u5e03\u306b\u95a2\u3059\u308b\u901a\u5e38\u306e\u6587\u306f\u3001Hilbertraum-s-sypei\u88fd\u54c1\u306b\u9069\u7528\u3055\u308c\u307e\u3059\u3002 Hi{displaystyle h_ {i}} \u8981\u7d20\u306e\u3042\u308b\u30d2\u30eb\u30d0\u30fc\u306e\u5922 xi{displaystyle x_ {i}} \u306a\u308c\uff1a H1\u2297 H2\u2245 H2\u2297 H1{displaystyle h_ {1} otimes h_ {2} cong h_ {2} otimes h_ {1}} \u3068 x1\u2297 x2\u21a6 x2\u2297 x1{displaystyle x_ {1} otimes x_ {2} mapsto x_ {2} otimes x_ {1}}} H1\u2297 \uff08 H2\u2297 H3\uff09\uff09 \u2245 \uff08 H1\u2297 H2\uff09\uff09 \u2297 H3{displaystyle h_ {1} otimes\uff08h_ {2} otimes h_ {3}\uff09cong\uff08h_ {1} otimes h_ {2}\uff09otimes h_ {3}} \u3068 x1\u2297 \uff08 x2\u2297 x3\uff09\uff09 \u21a6 \uff08 x1\u2297 x2\uff09\uff09 \u2297 x3{displaystyle x_ {1} otimes\uff08x_ {2} otimes x_ {3}\uff09mapsto\uff08x_ {1} otimes x_ {2}\uff09otimes x_ {3}} H1\u2297 \uff08 H2\u2295 H3\uff09\uff09 \u2245 \uff08 H1\u2297 H2\uff09\uff09 \u2295 \uff08 H1\u2297 H3\uff09\uff09 {displaystyle h_ {1} otimes\uff08h_ {2} oplus h_ {3}\uff09cong\uff08h_ {1} otimes h_ {2}\uff09oplus\uff08h_ {1} otimes h_ {3}\uff09}} \u3068 x1\u2297 \uff08 x2\u2295 x3\uff09\uff09 \u21a6 \uff08 x1\u2297 x2\uff09\uff09 \u2295 \uff08 x1\u2297 x3\uff09\uff09 {displaystyle x_ {1} otimes\uff08x_ {2} oplus x_ {3}\uff09mapsto\uff08x_ {1} otimes x_ {2}\uff09oplus\uff08x_ {1} otimes x_ {3}\uff09} Hilbertraum-Human\u88fd\u54c1\u306b\u306f\u3001\u3044\u308f\u3086\u308b\u30af\u30ed\u30b9\u30b9\u30bf\u30f3\u30c0\u30fc\u30c9\u30d7\u30ed\u30d1\u30c6\u30a3\u304c\u3042\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u9069\u7528\u3055\u308c\u307e\u3059 \u2016 \u30d0\u30c4 \u2297 \u3068 \u2016 = \u2016 \u30d0\u30c4 \u2016 de \u2016 \u3068 \u2016 {displaystyle | xotimes y | = | x | cdot | y |} \u3059\u3079\u3066\u306e\u30d9\u30af\u30c8\u30eb\u7528 \u30d0\u30c4 {displaystyle x} \u3068 \u3068 {displaystyle y} \u30d8\u30eb\u30d7\u30eb\u30fc\u30e0\u304b\u3089\u3002 \u305f\u3081\u306b \u30d0\u30c4 \u2208 h {displaystyle\u3092\u304a\u9858\u3044\u3057\u307e\u3059 \u3068 \u3068 \u2208 k {displaystyle yin k} \u7dda\u5f62\u6f14\u7b97\u5b50\u3068\u3057\u3066\u306e\u4e8c\u9805\u7a4d\u306e\u610f\u5473\u3067\u306e\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306f\u3067\u304d\u307e\u3059\u304b \u30d0\u30c4 \u2297 \u3068 \uff1a k \u2192 h {displaystyle xotimes yolon kto h} \u7406\u89e3\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6f14\u7b97\u5b50\u306e\uff08\u4ee3\u6570\uff09\u7dda\u5f62\u30b7\u30a7\u30eb\u306f\u3001\u6f14\u7b97\u5b50\u306e\u6709\u9650\u30e9\u30f3\u30af\u306e\u4ee3\u6570\u3067\u3042\u308a\u3001\u3053\u308c\u306fFr\u00e9chetRiesz\u306e\u6587\u304b\u3089\u7d9a\u304d\u307e\u3059\u3002\u4e0a\u8a18\u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u306f\u3001\u305d\u308c\u3092\u8a98\u5c0e\u3059\u308b\u3060\u3051\u3067\u3059 hilbert-schmidt-norm \u305d\u3057\u3066\u3001\u6709\u9650\u30e9\u30f3\u30af\u306e\u6f14\u7b97\u5b50\u306f \u30d2\u30eb\u30d0\u30fc\u30c8\u30b9\u30df\u30b9\u30aa\u30da\u30ec\u30fc\u30bf\u30fc \u3053\u308c\u306f\u5b8c\u5168\u306b\u3053\u306e\u6a19\u6e96\u306e\u89b3\u70b9\u304b\u3089\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u306e\u6709\u9650\u30e9\u30f3\u30af\u306e\u5b8c\u4e86\u304c\u3001\u306e\u30d2\u30eb\u30d0\u30fc\u30c8\u30b7\u30e5\u30df\u30c3\u30c8\u30aa\u30d1\u30fc\u30bf\u30fc\u30ba\u306e\u90e8\u5c4b\u306b\u3059\u304e\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002 k {displaystyle k} \u5f8c h {displaystyle h} \u3002 \u306a\u308c L2\uff08 X1\u3001 \u03a31\u3001 \u03bc1\uff09\uff09 {displaystyle l^{2}\uff08x_ {1}\u3001sigma _ {1}\u3001mu _ {1}\uff09} \u3068 L2\uff08 X2\u3001 \u03a32\u3001 \u03bc2\uff09\uff09 {displaystyle l^{2}\uff08x_ {2}\u3001sigma _ {2}\u3001mu _ {2}\uff09} l 2  – \u30eb\u30fc\u30e0\u3082 a {displaystyle sigma}  – \u30a2\u30e9\u30f3\u30c7\u30f3\u30b9\u3002\u6b21\u306b\u3001hilbertraum-speitrodukt isomorph\u3067\u3059 L2{displaystyle l^{2}}  – \u30e1\u30b8\u30e3\u30fc\u306e\u7a4d\u306e\u30d7\u30e9\u30a6\u30e0\u3001\u3064\u307e\u308a [\u521d\u3081] L2(X1,\u03a31,\u03bc1)\u2297L2(X2,\u03a32,\u03bc2)\u2245L2(X1\u00d7X2,\u03a31\u2297\u03a32,\u03bc1\u00d7\u03bc2){displaystyle l^{2}\uff08x_ {1}\u3001sigma _ {1}\u3001mu _ {1}\uff09otimes l^{2}\uff08x_ {2}\u3001sigma _ {2}\u3001mu _ {2}\uff09cong l^{2}\uff08x_ {1} time x_ {1} sigma _ {1} time x_ {1} _ {2}\u3001mu _ {1}\u56demu _ {2}\uff09} \u21132(I)\u2297\u21132(J)\u2245\u21132(I\u00d7J){displaySyle he ^{2}\uff08i\uff09otimes ell ^{2}\uff08j\uff09cong ^{2}\uff08ittimes j\uff09} \u3002 \u3053\u308c\u306f\u3001Hilbert Schmidt\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u304c\u6b63\u65b9\u5f62\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u4fc2\u6570\u3092\u6301\u3064\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u3067\u3042\u308b\u305f\u3081\u3001\u5f53\u3066\u306f\u307e\u308a\u307e\u3059\u3002 Fischer-Riesz\u306e\u5224\u6c7a\u306b\u3088\u308b\u3068\u3001\u3059\u3079\u3066\u306e\u30d2\u30eb\u30d0\u30fc\u306f\u5922\u3092\u898b\u3066\u3044\u307e\u3059 \u21132\uff08 \u79c1 \uff09\uff09 {displaystyle ell ^{2}\uff08i\uff09} \u9069\u5207\u306a \u79c1 {displaystyle i} \u306f\u3001\u30d2\u30eb\u30d0\u30fc\u306e\u5922\u306b\u5f93\u3044\u307e\u3059 h {displaystyle h} \u3068 k \uff1a {displaystyle k\uff1a} dim(H\u2297K)=dim(H)\u22c5dim(K),{displaystyle mathrm {dim}\uff08hotimes k\uff09\u3001=\u3001mathrm {dim}\uff08h\uff09cdot mathrm {dim}\uff08k\uff09,,} \u3057\u305f\u304c\u3063\u3066 dim\uff08 h \uff09\uff09 {displaystyle mathrm {dim}\uff08h\uff09} \u30d2\u30eb\u30d0\u30fc\u30c8\u30c9\u30ea\u30fc\u30e0\u30c7\u30a3\u30e1\u30f3\u30b7\u30e7\u30f3\u3001\u3064\u307e\u308aH.\u306e\u4efb\u610f\u306e\u30aa\u30eb\u30bd\u30eb\u30de\u30eb\u30d9\u30fc\u30b9\u306e\u30ab\u30fc\u30c7\u30a3\u30ca\u30ea\u30c6\u30a3 h {displaystyle h} \u30b9\u30bf\u30f3\u30c9\u3002 \u306a\u308c h {displaystyle h} \u3068 k {displaystyle k} \u30d2\u30eb\u30d0\u30fc\u306e\u5922\u3068 \uff08 \u3068 j\uff09\uff09 j\u2208J{displaystyle\uff08y_ {j}\uff09_ {jin j}} \u306e\u30aa\u30eb\u30bd\u30fc\u30de\u30eb\u30d9\u30fc\u30b9\u306b\u306a\u308a\u307e\u3059 k {displaystyle k} \u3002\u305d\u308c\u304b\u3089 h \u2297 yj\uff1a= { \u30d0\u30c4 \u2297 yj; \u30d0\u30c4 \u2208 h } \u2282 h \u2297 k {displaystyle hotimes y_ {j}\uff1a= {xotimes y_ {j}; xin h} subset hotetimes k} 1\u3064\u3082 h {displaystyle h} \u540c\u578b\u6c34\u4e2d\u7b49\u5c3a\u6027\u3068\u305d\u3046\u3067\u3059 h \u2297 k \u2245 \u2a01j\u2208Jh \u2297 yj{displaystyle hotimes kcong bigoplus _ {jin j} hotimes y_ {j}} \u3001 \u53f3\u5074\u306f\u76f4\u4ea4\u5408\u8a08\u3068\u3057\u3066\u8aad\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u306e\u5f79\u5272 h {displaystyle h} \u3068 k {displaystyle k} \u3082\u3061\u308d\u3093\u4ea4\u63db\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u610f\u5473\u3067\u3001\u30d2\u30eb\u30d9\u30eb\u30c8\u30e9\u30a6\u30e0\u3068\u4eba\u9593\u306e\u88fd\u54c1\u306f\u3001\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306e2\u3064\u306e\u8981\u56e0\u306e1\u3064\u306e\u9069\u5207\u306a\u76f4\u63a5\u7684\u306a\u30b3\u30d4\u30fc\u306b\u3059\u304e\u307e\u305b\u3093\u3002 [3] \u5b9a\u6570\u7dda\u5f62\u6f14\u7b97\u5b50 a \u2208 l \uff08 h \uff09\uff09 {displaystyle ain l\uff08h\uff09} \u3068 b \u2208 l \uff08 k \uff09\uff09 mmslaves ylexle\u306fhorh\u3067\u3057\u305f\uff08u\u3002 \u30d2\u30eb\u30d0\u30fc\u30b9\u30c8\u30ea\u30fc\u30e0\u3067 h {displaystyle h} \u3068 k {displaystyle k} \u81ea\u5206\u81ea\u8eab\u3092\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306b\u3057\u307e\u3057\u3087\u3046 a \u2297 b {displaystyle aotimes b} \u306e\u4e0a h \u2297 k {displaystyle hotimesk} \u307e\u3068\u3081\u308b\u3002\u3088\u308a\u6b63\u78ba\u306a\uff1a \u4ee3\u6570\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1 a \u2299 b \uff1a h \u2299 k \u2192 h \u2299 k {displaystyle aodot b\uff1ahodot krightarrow hodot k} \u5ba3\u6559\u53ef\u80fd\u306a\u5922\u306e\u57fa\u6e96\u306b\u95a2\u3057\u3066\u7740\u5b9f\u306b\u3042\u308b\u305f\u3081\u3001\u5b89\u5b9a\u3057\u305f\u7dda\u5f62\u6f14\u7b97\u5b50\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059 a \u2297 b \u2208 l \uff08 h \u2297 k \uff09\uff09 {displaystyle aotimes b\u3001in\u3001l\uff08hotimes k\uff09} \u7d9a\u3051\u3089\u308c\u307e\u3059\u3002\u4ee5\u4e0b\u304c\u9069\u7528\u3055\u308c\u307e\u3059 \u2016 a \u2297 b \u2016 = \u2016 a \u2016 de \u2016 b \u2016 {displaystyle | aotimes b | = | a | cdot | b |} \u3001\u3053\u3053\u3067\u3001\u5de6\u5074\u306e\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u30d5\u30a9\u30fc\u30e0 l \uff08 h \u2297 k \uff09\uff09 {displaystyle l\uff08hotimes k\uff09} \u30b9\u30bf\u30f3\u30c9\u3002 [4] \u3053\u308c\u306f\u3001\u30d8\u30eb\u30d7\u306e\u5922\u306e\u305f\u3081\u306e\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u3092\u5c0e\u5165\u3059\u308b\u305f\u3081\u306e\u6700\u3082\u91cd\u8981\u306a\u52d5\u6a5f\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u6f14\u7b97\u5b50\u306b\u3088\u3063\u3066 a \u2297 b {displaystyle aotimes b} Von-Neumann Alleys\u306e\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002 \u304b\u3089\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u3092\u691c\u8a0e\u3057\u307e\u3059 \u2113 2{displaystyle ell ^{2}} \u3042\u306a\u305f\u81ea\u8eab\u3068\u3002\u3059\u3079\u3066\u306e\u8981\u7d20 t = \u2211i=1nxi\u2297 yi{displaystyle textStyle t = sum _ {i = 1}^{n} x_ {i} otimes y_ {i}} \u4ee3\u6570\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306f\u3001\u6700\u7d42\u7684\u306b\u5bf8\u6cd5\u6f14\u7b97\u5b50\u306b\u6a5f\u4f1a\u3092\u63d0\u4f9b\u3057\u307e\u3059 Tt\uff1a \u21132\u2192 \u21132\u3001 \u30d0\u30c4 \u21a6 \u2211i=1n\u27e8 \u30d0\u30c4 \u3001 yi\u27e9 xi{displaystyle textStyle t_ {t} colon ell ^{2} rightArrow ell ^{2} ,, xmapsto sum _ {i = 1} ^{n} langle x\u3001y_ {i} rangle x_ {i}}} \u3001\u3064\u307e\u308a\u3001\u4ee3\u6570\u7684\u306a\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u306f\u81ea\u7136\u306b\u3042\u308a\u307e\u3059 l \uff08 \u2113 2\uff09\uff09 {displaysyle l\uff08he ^{2}\uff09} \u542b\u3080\u3002\u8aac\u660e \u2297 \u03b5{displaystyle otimes _ {varepsilon}} \u3068 \u2297 \u03c0{displaystyle otimes _ {pi}} \u6ce8\u5c04\u307e\u305f\u306f\u5c04\u5f71\u30c6\u30f3\u30bd\u30eb\u88fd\u54c1\u304c\u53d6\u5f97\u3055\u308c\u307e\u3059\u3002 \u3053\u308c\u306f\u3001\u3068\u308a\u308f\u3051\u3001\u4ee5\u4e0b\u306eR. Schatten\u306e\u6559\u79d1\u66f8\u3067\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u2191  R.V. Kadison\u3001J\u3002R\u3002Ringrose\uff1a \u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u4ee3\u6570\u306e\u7406\u8ad6\u306e\u57fa\u790e \u30011983\u3001ISBN 0123933013\u3001\u4f8b2.6.11  \u2191  R.V. Kadison\u3001J\u3002R\u3002Ringrose\uff1a \u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u4ee3\u6570\u306e\u7406\u8ad6\u306e\u57fa\u790e \u30011983\u3001ISBN 0123933013\u3001\u4f8b2.6.10  \u2191  R.V. Kadison\u3001J\u3002R\u3002Ringrose\uff1a \u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u4ee3\u6570\u306e\u7406\u8ad6\u306e\u57fa\u790e \u30011983\u3001ISBN 0123933013\u3001\u5099\u80032.6.8  \u2191  Jacques Dixmier\uff1a \u30ce\u30a4\u30de\u30f3\u4ee3\u6570\u306b\u3088\u3063\u3066\u3002 \u30ce\u30fc\u30b9\u30db\u30e9\u30f3\u30c9\u3001\u30a2\u30e0\u30b9\u30c6\u30eb\u30c0\u30e01981\u3001ISBN 0-444-86308-7\u3001i.2.3        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/11082#breadcrumbitem","name":"Hilbertraum Tense Product -Wikipedia"}}]}]